The conjugation operator on .
The construction of a function given by moments. (La construction de quelque fonction par des moments donnés.)
The Dirichlet-Jordan theorem for the Henstock-Fourier transform.
The discrete Fourier-Transform an Lp approximation of functions.
The divergence phenomena of interpolation type operators in space
The Euler Maclaurin Expansion for the Cauchy Principal Value Integral.
The Fourier Character Of Series With Slowly Varying Convergence Moduli
The Fourier integral for a certain class of distributions
The aim of this paper is to derive by elementary means a theorem on the representation of certain distributions in the form of a Fourier integral. The approach chosen was found suitable especially for students of post-graduate courses at technical universities, where it is in some situations necessary to restrict a little the extent of the mathematical theory when concentrating on a technical problem.
The Fourier transform in Lebesgue spaces
For each () it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each , a norm is defined so that the space of Fourier transforms is isometrically isomorphic to . There is an exchange theorem and inversion in norm.
The Fourier transform in weighted spaces
The Fourier transform of functions satisfying the Lipschitz condition on rank 1 symmetric spaces.
The Fourier transform on quantum Euclidean space.
The Fourier transforms of Lipschitz functions on the Heisenberg group.
The functional equation F(ax) + F(bx+a) = F(bx) + F(ax+b), entire and almost periodic solutions.
The general chain transform and self-reciprocal functions.
The General Recurrence Relation for Divided Differences and the General Newton-Interpolation-Algorithm With Applications to Trigonometric Interpolation.
The generalized almost periodic part of an ergodic function
The Gibbs phenomenon and Lebesgue constants for regular means
The harmonic Cesáro and Copson operators on the spaces , 1 ≤ p ≤ 2
The harmonic Cesàro operator is defined for a function f in for some 1 ≤ p < ∞ by setting for x > 0 and for x < 0; the harmonic Copson operator ℂ* is defined for a function f in by setting for x ≠ 0. The notation indicates that ℂ and ℂ* are adjoint operators in a certain sense. We present rigorous proofs of the following two commuting relations: (i) If for some 1 ≤ p ≤ 2, then a.e., where f̂ denotes the Fourier transform of f. (ii) If for some 1 < p ≤ 2, then a.e. As...
The Hilbert transform in weighted spaces of integrable vector-valued functions